3-uniform hypergraphs avoiding a given odd cycle

Abstract

We give upper bounds for the size of 3-uniform hypergraphs avoiding a given odd cycle using the definition of a cycle due to Berge. In particular, we show that a 3-uniform hypergraph containing no cycle of length 2k+1 has less than 4k 4 n 1+1/k+O(n) edges. Constructions show that these bounds are best possible (up to constant factor) for k=1,2,3, 5.

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Correspondence to Ervin Győri.

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Research partially supported by the Hungarian OTKA Grant AT 48826 and by ToK project FIST of Rényi Institute in the 6th Framework Program of the European Union.

Research partially supported by ToK project FIST of Rényi Institute in the 6th Framework Program of the European Union.

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Győri, E., Lemons, N. 3-uniform hypergraphs avoiding a given odd cycle. Combinatorica 32, 187–203 (2012). https://doi.org/10.1007/s00493-012-2584-4

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Mathematics Subject Classification (2000)

  • 05C65